liverpool2044
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#1
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http://www.mei.org.uk/files/papers/2011_June_c4.pdf

im usually okay at vectors but i dont understand 7ii

i get you have to find the angle between the normal vector but it then says horizontal plane, why is this 0 0 1

thanks in advance
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ak111
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You have to take the normal vector of both and find the angle between them. (0,0,1) is the normal vector of the horizontal plane (z=0)
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liverpool2044
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(Original post by ak111)
You have to take the normal vector of both and find the angle between them. (0,0,1) is the normal vector of the horizontal plane (z=0)
where does the 0 0 1 come from though i dont really get it
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ak111
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(Original post by liverpool2044)
where does the 0 0 1 come from though i dont really get it
The ground level is represented here as the plane 0x+0y+z=0 (same as z=0). To find the normal vector you always take the coefficients of the x,y and z. The coefficient of x is 0, y is 0 and z is 1 so we get the normal vector to this horizontal plane as (0,0,1)
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liverpool2044
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(Original post by ak111)
The ground level is represented here as the plane 0x+0y+z=0 (same as z=0). To find the normal vector you always take the coefficients of the x,y and z. The coefficient of x is 0, y is 0 and z is 1 so we get the normal vector to this horizontal plane as (0,0,1)
why is z the horizontal plane wouldnt that be x?
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ak111
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(Original post by liverpool2044)
why is z the horizontal plane wouldnt that be x?
It lies on the x axis but that doesn't make x the horizontal plane. If you think about all the points on the plane, x and y are always changing as you move around the plane but z is always 0 at all points on that plane so the plane has to be z=0.
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liverpool2044
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(Original post by ak111)
It lies on the x axis but that doesn't make x the horizontal plane. If you think about all the points on the plane, x and y are always changing as you move around the plane but z is always 0 at all points on that plane so the plane has to be z=0.
ahh okay sorry im being useless here, how do you actually get 0 0 1 then i know you said coefficients but surely the ground level is just zero for all
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liverpool2044
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ak111
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(Original post by liverpool2044)
ahh okay sorry im being useless here, how do you actually get 0 0 1 then i know you said coefficients but surely the ground level is just zero for all
Yes the ground level is 0 for z but the normal vector has to be 0,0,1 as it is normal to the plane
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liverpool2044
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#10
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(Original post by ak111)
Yes the ground level is 0 for z but the normal vector has to be 0,0,1 as it is normal to the plane
finding angle between normal vector and k - it says you get a mark for that

so its the normal vector with k? k is the coordinate on d so can it be worked out from there
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